The primary objective is to assess safety of four dose levels of MEDI-507 combined with methylprednisolone for initial treatment of at least grade II acute GVHD in stem cell or bone marow allograft recipients. The secondary objectives are: 1) To evaluate the effect of MEDI-507 administration on the absolute lymphocyte count and the dynamics of lymphocyte phenotypes CD3 and CD16(+)56(+) 2) To describe serum concentrations and pharmacokinetics of MEDI-507 in GVHD patients 3) To describe CD2 receptor occupancy by MEDI-507 4) To describe the change in organ stage and GVHD grade at 12,30,44,60, and 100 days following treatment 5) To describe the total dose of corticosteroids administered for 30 days 6) To describe MEDI-507 immunogenicity 7) To describe survival and the occurrence of chronic GVHD, opportunistic infections, malignancy and lymphoproliferative disorder until Study Day 364. Treatment: Study therapy consist of study drug (placebo or MEDI-507) administered with corticosteroids. Intravenous methylprednisolone (at least 2mg/kg/day) must be administered between eight and 24 hours prior to the initial study drug infusion and for at least 72 hours after initial receipt of study drug. Methylprednisolone (at least 2mg/kg/day) may be started up to 72 hours prior to receipt of study drug. An equivalent dose of oral or IV corticosteroid may be substituted for methylprednisolone 72 hours after initial study drug. The total duration of corticosteroid treatment must be at least ten days. The study drug will be administered intravenously on study Days 0,3,6, and 9.